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> Part B3 
COMPLEX WAVELETS AND ITS APPLICATION TO IMAGE FUSION 
Xu Qing, Xing Shuai, Tan Bing, Li Jiansheng, Geng Zexun 
Department of Remote Sensing Information Engineering, Zhengzhou Institute of Surveying and Mapping, No.66 
Longhai Middle Road, 450052, ZhengZhou City, Henan Province, China-(xuging, xingshuai)@chxy.com 
Commission III, WG III/6 
KEY WORDS: Algorithms, Multiresolution analysis, Image fusion, Multispectral, Remote sensing 
ABSTRACT: 
Image fusion deals with the integration of remote sensing images from various sensors, with multi-spectrum and high-spectrum, 
multi-angle viewing and multi-resolutions, aiming at achieving improved image quality (o better support improved image 
classification, monitoring and etc. The main goal of this paper is to intraduce a new approach to fuse panchromatic image and 
multi-spectral images by complex wavelet. First, the theoretical basis of complex wavelet is described together with its key 
properties(e.g. approximate shift invariance, good directional selectivity, perfect reconstruction(PR), limited redundancy and efficient 
order-N computation). Secondly, the new method for fusing remote sensing images based on complex wavelet is proposed. Finally 
experiment results show that the fusion method based on complex wavelet transform is remarkably better than the fusion method 
based on classical discrete wavelet transform. 
® Poor directional selectivity for diagonal features, because 
1. INRTRODUCTION the wavelet features are separable and real. 
Nick Kingsbury has introduced the Dual-Tree Complex 
Wavelet Transform (DT CWT), which has the following 
properties (N. Kingsbury, 1998a): 
€ Approximate shift invariance; 
€ (Good directional selectivity in 2-dimensions (2-D) with 
Gabor-like filters also true for higher dimensionality: 
Image fusion deals with multi-sensors, multi-spectrum, 
multi-angle viewing and multi-resolutions remote sensing 
images from various, with, aiming at achieving improved image 
quality to better support improved image classification, 
monitoring and etc. Fused image will enhance reliability and 
speed of feature extraction, increase the usage of the data sets, 
me ; Lui : m-D); 
and extend remote sensing images' application area. There have : : ; 
à = : a : € Perfect reconstruction (PR) using short linear-phase 
been a lot of research efforts on image fusion, and many fusion fil 
ilters; 
methods have been proposed. However, these image fusion iit. : ; 
prop : - € Limited redundancy: independent of the number of scales: 
alvsis and applicati 2:1 for 1-D (2" :| for m-D); 
ee € Efficient order-N computation - only twice the simple 
DWT for 1-D (2” times for m-D); 
methods are not enough and cause some difficulties for image 
The advantages of wavelet transform is that it can analyze signal 
M Hie domain sui A e pen and fre The CWT has shown good performance in image restoration 
multi-resolution analysis is similar with Human Vision System. and denoisinz (A: Jalobeani's, 2000; Nick Kjneshorvril998b; 
Toe Disciete Servelet, Tiausform (DWT) sn its pans Peter de Rivaz 2001), motion estimation (Julian Magarey 
decimated form established by Mallat (S S Mallat, 1989) is 1998). image elassification (Serken Halipaghy 1999), texture 
widely used in image processing now. If we fuse a high analysis Cavier Porte; 1999; N. Kingshury, 1998; Sorkon 
resolution panchromatic image and a multi-spectral image by Hatipoglu, 1999), image enhäncement (Nick KingsburyEl998b), 
DWT, the fused image can conserve more spectral image matching GIANG Hau-ping , 2000). 
characteristics of the multi-spectral image. So the fusion method = 
based on DWT. is-fequentiy used and become ong of iin In this paper, we propose a image fusion method based on CWT 
fusion methods. But the DWT has two main disadvantages (N. multi-resolution analysis. Experiment results show that the 
Kinssburs, 19952): LR quality of fusion image based on CWT is better than fusion 
® Lack of shift invariance. This means that small shifts in image bused on DWT. 
the input signal ean cause major variations in the 
distribution of energy between DWT coefficients at 
different scales, 
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